Mensuration

1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Answer: Perimeter of Square = 4 x side = 4 x 60 = 240 sq metres

Area of Square = Side² = 60² = 3600 square metre

Perimeter of Rectangle = 2(length + breadth)

Or, 240 = 2(80 + breadth)

Or, 80 + breadth = 120

Or, breadth = 120-80 = 40 metres

Area of rectangle = length x breadth = 80 x 40 = 3200 square metres

Now it is clear that the area of the square field is greater than the area of the rectangular field.

2. Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs 55 per m².

Answer: Area of the square plot = Side² = 25² = 625 square metre

Area of the house construction part = length x breadth

= 20 x 15 = 300 sq m

So, area of the garden = 625-300=325 square metre

Cost of developing the garden = Area x Rate

= 300 x 55 = 16500 rupees

3. The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 – (3.5 + 3.5) metres].

Answer: Area of the rectangular part = length x breadth

= 20 x 7 = 140 sq m

Area of Semicircular portions: = п x r2

Perimeter of the shape = 22 + 20 + 20 = 62 metres

4. A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 m2? (If required you can split the tiles in whatever way you want to fill up the corners).

Answer: Area of the Parallelogram = base x height

= 24 x 10 = 240 sq cm

(area of floor is converted into square cms)

5. An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.

So, the food shape in (a) requires the ant to cover the least distance.